{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Laminar pipe flow - Hagen–Poiseuille solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we use icoFoam to compute a laminar pipe flow, then we compare the numerical solution with the analytical solution. <br>\n",
    "\n",
    "You will find the instructions of how to run this case in the file README.FIRST. <br>\n",
    "\n",
    "By the way, to plot the numerical solution you need to use the utility sample to get the solution at the end of the pipe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.loadtxt('../postProcessing/sampleDict/20/s2_U.xy', skiprows=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f86699e3650>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hT3CO2XjorozsXJJmaHlBkcKk0i0ix7Q5LQOAcHJ5IfIlOoYv46HsAYxJb+84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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8669d5ef90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure(figsize=(12,8))\n",
    "\n",
    "data=np.loadtxt('../postProcessing/sampleDict/20/s2_U.xy', skiprows=0)\n",
    "\n",
    "plt.plot(data[:,0],data[:,1],'o',label='icoFoam')\n",
    "\n",
    "vmax = max(data[:,1])\n",
    "rmax = 0.5\n",
    "\n",
    "x = np.linspace(-1*rmax, rmax, 100)\n",
    "sol = vmax*(1 - x**2/rmax**2)\n",
    "\n",
    "plt.plot(x,sol,'-',label='Analytical solution')\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.xlabel('Radius',fontsize=15)\n",
    "plt.ylabel('$V_{axial}$',fontsize=15)\n",
    "\n",
    "\n",
    "\n",
    "#To save a figure\n",
    "#plt.savefig('test.png', format='png', dpi=300)\n",
    "#plt.savefig('test.pdf', format='pdf', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
